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//$$ sort.cpp Sorting
// Copyright (C) 1991,2,3,4: R B Davies
#define WANT_MATH
#include "include.h"
#include "config.h"
#include "newmatap.h"
#ifdef use_namespace
namespace NEWMAT {
#endif
#ifdef DO_REPORT
#define REPORT { static ExeCounter ExeCount(__LINE__,13); ++ExeCount; }
#else
#define REPORT {}
#endif
/******************************** Quick sort ********************************/
// Quicksort.
// Essentially the method described in Sedgewick s algorithms in C++
// My version is still partially recursive, unlike Segewick s, but the
// smallest segment of each split is used in the recursion, so it should
// not overlead the stack.
// If the process does not seems to be converging an exception is thrown.
#define DoSimpleSort 17 // when to switch to insert sort
#define MaxDepth 50 // maximum recursion depth
static void MyQuickSortDescending(Real* first, Real* last, int depth);
static void InsertionSortDescending(Real* first, const int length,
int guard);
static Real SortThreeDescending(Real* a, Real* b, Real* c);
static void MyQuickSortAscending(Real* first, Real* last, int depth);
static void InsertionSortAscending(Real* first, const int length,
int guard);
void SortDescending(GeneralMatrix& GM)
{
REPORT
Tracer et("QuickSortDescending");
Real* data = GM.Store(); int max = GM.Storage();
if (max > DoSimpleSort) MyQuickSortDescending(data, data + max - 1, 0);
InsertionSortDescending(data, max, DoSimpleSort);
}
static Real SortThreeDescending(Real* a, Real* b, Real* c)
{
// sort *a, *b, *c; return *b; optimise for already sorted
if (*a >= *b)
{
if (*b >= *c) { REPORT return *b; }
else if (*a >= *c) { REPORT Real x = *c; *c = *b; *b = x; return x; }
else { REPORT Real x = *a; *a = *c; *c = *b; *b = x; return x; }
}
else if (*c >= *b) { REPORT Real x = *c; *c = *a; *a = x; return *b; }
else if (*a >= *c) { REPORT Real x = *a; *a = *b; *b = x; return x; }
else { REPORT Real x = *c; *c = *a; *a = *b; *b = x; return x; }
}
static void InsertionSortDescending(Real* first, const int length,
int guard)
// guard gives the length of the sequence to scan to find first
// element (eg = length)
{
REPORT
if (length <= 1) return;
// scan for first element
Real* f = first; Real v = *f; Real* h = f;
if (guard > length) { REPORT guard = length; }
int i = guard - 1;
while (i--) if (v < *(++f)) { v = *f; h = f; }
*h = *first; *first = v;
// do the sort
i = length - 1; f = first;
while (i--)
{
Real* g = f++; h = f; v = *h;
while (*g < v) *h-- = *g--;
*h = v;
}
}
static void MyQuickSortDescending(Real* first, Real* last, int depth)
{
REPORT
for (;;)
{
const int length = last - first + 1;
if (length < DoSimpleSort) { REPORT return; }
if (depth++ > MaxDepth)
Throw(ConvergenceException("QuickSortDescending fails: "));
Real* centre = first + length/2;
const Real test = SortThreeDescending(first, centre, last);
Real* f = first; Real* l = last;
for (;;)
{
while (*(++f) > test) {}
while (*(--l) < test) {}
if (l <= f) break;
const Real temp = *f; *f = *l; *l = temp;
}
if (f > centre)
{ REPORT MyQuickSortDescending(l+1, last, depth); last = f-1; }
else { REPORT MyQuickSortDescending(first, f-1, depth); first = l+1; }
}
}
void SortAscending(GeneralMatrix& GM)
{
REPORT
Tracer et("QuickSortAscending");
Real* data = GM.Store(); int max = GM.Storage();
if (max > DoSimpleSort) MyQuickSortAscending(data, data + max - 1, 0);
InsertionSortAscending(data, max, DoSimpleSort);
}
static void InsertionSortAscending(Real* first, const int length,
int guard)
// guard gives the length of the sequence to scan to find first
// element (eg guard = length)
{
REPORT
if (length <= 1) return;
// scan for first element
Real* f = first; Real v = *f; Real* h = f;
if (guard > length) { REPORT guard = length; }
int i = guard - 1;
while (i--) if (v > *(++f)) { v = *f; h = f; }
*h = *first; *first = v;
// do the sort
i = length - 1; f = first;
while (i--)
{
Real* g = f++; h = f; v = *h;
while (*g > v) *h-- = *g--;
*h = v;
}
}
static void MyQuickSortAscending(Real* first, Real* last, int depth)
{
REPORT
for (;;)
{
const int length = last - first + 1;
if (length < DoSimpleSort) { REPORT return; }
if (depth++ > MaxDepth)
Throw(ConvergenceException("QuickSortAscending fails: "));
Real* centre = first + length/2;
const Real test = SortThreeDescending(last, centre, first);
Real* f = first; Real* l = last;
for (;;)
{
while (*(++f) < test) {}
while (*(--l) > test) {}
if (l <= f) break;
const Real temp = *f; *f = *l; *l = temp;
}
if (f > centre)
{ REPORT MyQuickSortAscending(l+1, last, depth); last = f-1; }
else { REPORT MyQuickSortAscending(first, f-1, depth); first = l+1; }
}
}
//********* sort diagonal matrix & rearrange matrix columns ****************
// used by SVD
// these are for sorting singular values - should be updated with faster
// sorts that handle exchange of columns better
// however time is probably not significant compared with SVD time
void SortSV(DiagonalMatrix& D, Matrix& U, bool ascending)
{
REPORT
Tracer trace("SortSV_DU");
int m = U.Nrows(); int n = U.Ncols();
if (n != D.Nrows()) Throw(IncompatibleDimensionsException(D,U));
Real* u = U.Store();
for (int i=0; i<n; i++)
{
int k = i; Real p = D.element(i);
if (ascending)
{
for (int j=i+1; j<n; j++)
{ if (D.element(j) < p) { k = j; p = D.element(j); } }
}
else
{
for (int j=i+1; j<n; j++)
{ if (D.element(j) > p) { k = j; p = D.element(j); } }
}
if (k != i)
{
D.element(k) = D.element(i); D.element(i) = p; int j = m;
Real* uji = u + i; Real* ujk = u + k;
if (j) for(;;)
{
p = *uji; *uji = *ujk; *ujk = p;
if (!(--j)) break;
uji += n; ujk += n;
}
}
}
}
void SortSV(DiagonalMatrix& D, Matrix& U, Matrix& V, bool ascending)
{
REPORT
Tracer trace("SortSV_DUV");
int mu = U.Nrows(); int mv = V.Nrows(); int n = D.Nrows();
if (n != U.Ncols()) Throw(IncompatibleDimensionsException(D,U));
if (n != V.Ncols()) Throw(IncompatibleDimensionsException(D,V));
Real* u = U.Store(); Real* v = V.Store();
for (int i=0; i<n; i++)
{
int k = i; Real p = D.element(i);
if (ascending)
{
for (int j=i+1; j<n; j++)
{ if (D.element(j) < p) { k = j; p = D.element(j); } }
}
else
{
for (int j=i+1; j<n; j++)
{ if (D.element(j) > p) { k = j; p = D.element(j); } }
}
if (k != i)
{
D.element(k) = D.element(i); D.element(i) = p;
Real* uji = u + i; Real* ujk = u + k;
Real* vji = v + i; Real* vjk = v + k;
int j = mu;
if (j) for(;;)
{
p = *uji; *uji = *ujk; *ujk = p; if (!(--j)) break;
uji += n; ujk += n;
}
j = mv;
if (j) for(;;)
{
p = *vji; *vji = *vjk; *vjk = p; if (!(--j)) break;
vji += n; vjk += n;
}
}
}
}
#ifdef use_namespace
}
#endif
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